We're dividing 21101577 by 338 
We're looking to find how many times 338 goes into 21101577.

On to step 1:
2 divided by 338 is 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 338

Advancing to step 2:
338 can be fit into 21 0 times, resulting in a remainder of 21.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 21 after subtracting 0 from 21.
Bring next digit (1) of the dividend behind the 21 and repeat the process: 211 / 338

Let's proceed to step 3:
If we divide 211 by 338, we get 0 and a remainder of 211.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 211, we end up with 211.
Bring next digit (0) of the dividend behind the 211 and repeat the process: 2110 / 338

Step 4:
If we divide 2110 by 338, we get 6 and a remainder of 82.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Subtract 2028 from 2110 to get 82.
Grab the next digit (1) from the dividend, add it to 82, then carry on: 821 / 338

Step 5:
338 goes into 821 2 times with a remainder of 145.
Write down 2 as next digit of the result. 
Result so far: 62.0
Subtracting 676 from 821 leaves us with 145.
Bring next digit (5) of the dividend behind the 145 and repeat the process: 1455 / 338

Step 6:
When dividing 1455 by 338, we get 4 with a remainder of 103.
Write down 4 as next digit of the result. 
Result so far: 624.0
Deduct 1352 from 1455 and we're left with 103.
Include the next digit (7) from the dividend after 103, then repeat: 1037 / 338

On to step 7:
338 can be fit into 1037 3 times, resulting in a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 6243.0
If we subtract 1014 from 1037, we get 23.
Bring next digit (7) of the dividend behind the 23 and repeat the process: 237 / 338

Going ahead to step 8:
If we divide 237 by 338, we get 0 and a remainder of 237.
The next digit of our result is 0. 
Result so far: 62430.0
If we subtract 0 from 237, we get 237.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2370, and continue the process.

Let's proceed to step 9:
338 goes into 2370 7 times with a remainder of 4.
Put 7 as the next digit of the answer. 
Result so far: 62430.7
If we take 2366 away from 2370, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 10:
The number 338 fits into 40 0 times, leaving a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 62430.7
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 11:
338 can be fit into 400 1 times, resulting in a remainder of 62.
The next digit of our result is 1. 
Result so far: 62430.701
Subtract 338 from 400 to get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Step 12:
338 goes into 620 1 times with a remainder of 282.
Write down 1 as next digit of the result. 
Result so far: 62430.7011
The remainder is 282 after subtracting 338 from 620.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2820, and continue the process.

The final result is 62430.7011 with a remainder of 0.00282.